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Abstract

Five equations for system throughput capacity (1), governing all
non-growth, agent-directed systems are proposed and justified. Each equation
covers a specific system aspect. Any two or more of the equations can be
combined.
The equations are: a 'system sharing equation' that shows how (1) can be
maintained by reducing resources and increasing resource-sharing procedure
complexity, or vice versa.
A 'basic risk equation' that shows how expected (1) increases [decreases]
linearly with positive [negative] risk of loss of (1) in efficient
environments.
A 'preventive-resources risk equation' that shows how (1) is improved by
application of risk-preventing resources to reduce known risk.
A 'precautionary-procedure risk equation' that shows how (1) is improved by
use of precautionary procedures to reduce known risk.
A 'monitoring-procedure risk equation' that shows how (1) is improved by use
of a real-time monitoring procedure and risk-meaningful database to detect
unknown risk and reduce it with precautionary response procedures.
The conventional 'standard deviation risk measure with respect to mean' from
financial systems may be used, but a proposed new measure, called 'the
mean-expected loss measure with respect to hazard-free case', is shown to be
more appropriate for systems in general. The concept of an 'efficient
environment' is also proposed.
All quantities used in the equations are precisely defined and their units
specified. The equations reduce to numerical expressions, and can be
subjected to experimental test. The equations clarify and quantify basic
principles, enabling designers and operators of systems to reason correctly
about systems in complex situations. Spreng's Triangle, relating energy, time
and information follows from the sharing equation. The epirical
Markowitz-Sharpe-Lintner relationship betwen return, capital resources and
risk for financial systems follows from the basic risk equation.

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